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Title:Intertheoretic Reference in Mathematics
Author(s):Stidd, Sean Charles
Doctoral Committee Chair(s):Timothy McCarthy
Department / Program:Philosophy
Degree Granting Institution:University of Illinois at Urbana-Champaign
Abstract:Some mathematical terms are commonly taken by mathematicians, historians of mathematics, and ordinary speakers to co-refer with other mathematical terms even when each is embedded in a theory which predicates distinct properties of said referents. In this dissertation a picture of reference for such terms is set forth and defended which can make sense of such ordinary attributions of co-reference. It is argued that if one understands the perceivable structural properties of physical objects as mathematical entities, such properties can play the role of semantic anchors in the context of a hybrid internal-external ("descriptive"-"causal") theory of reference. The conditions under which two terms dominantly associated with such properties co-refer are developed, and it is argued that actual cases of co-reference which are not tractable on a structuralist approach meet these conditions. The ontological claim that some mathematical objects are perceivable structural properties of physical objects and the general semantic viewpoint of the dissertation are also given independent defense.
Issue Date:2006
Description:203 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.
Other Identifier(s):(MiAaPQ)AAI3243004
Date Available in IDEALS:2015-09-28
Date Deposited:2006

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